TSTP Solution File: ITP021+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ITP021+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:11:00 EDT 2023
% Result : Theorem 5.03s 5.22s
% Output : CNFRefutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 45
% Syntax : Number of formulae : 107 ( 24 unt; 31 typ; 0 def)
% Number of atoms : 224 ( 39 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 239 ( 91 ~; 112 |; 11 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-4 aty)
% Number of variables : 80 ( 0 sgn; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
bool: $i ).
tff(decl_23,type,
ne: $i > $o ).
tff(decl_24,type,
ind: $i ).
tff(decl_25,type,
arr: ( $i * $i ) > $i ).
tff(decl_26,type,
mem: ( $i * $i ) > $o ).
tff(decl_27,type,
ap: ( $i * $i ) > $i ).
tff(decl_28,type,
p: $i > $o ).
tff(decl_29,type,
k: ( $i * $i ) > $i ).
tff(decl_30,type,
i: $i > $i ).
tff(decl_31,type,
c_2Ebool_2ET: $i ).
tff(decl_32,type,
ty_2Eextreal_2Eextreal: $i ).
tff(decl_33,type,
c_2Eextreal_2Eextreal__le: $i ).
tff(decl_34,type,
c_2Ebool_2ECOND: $i > $i ).
tff(decl_35,type,
c_2Eextreal_2Eextreal__max: $i ).
tff(decl_36,type,
c_2Ebool_2EF: $i ).
tff(decl_37,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(decl_38,type,
c_2Ebool_2E_5C_2F: $i ).
tff(decl_39,type,
c_2Ebool_2E_2F_5C: $i ).
tff(decl_40,type,
c_2Ebool_2E_7E: $i ).
tff(decl_41,type,
c_2Emin_2E_3D: $i > $i ).
tff(decl_42,type,
c_2Ebool_2E_21: $i > $i ).
tff(decl_43,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_44,type,
epred2_3: ( $i * $i * $i ) > $o ).
tff(decl_45,type,
epred3_3: ( $i * $i * $i ) > $o ).
tff(decl_46,type,
epred4_3: ( $i * $i * $i ) > $o ).
tff(decl_47,type,
epred5_3: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_49,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk3_0: $i ).
tff(decl_51,type,
esk4_0: $i ).
tff(decl_52,type,
esk5_0: $i ).
fof(ap_tp,axiom,
! [X1,X2,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(boolext,axiom,
! [X5] :
( mem(X5,bool)
=> ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
fof(mem_c_2Eextreal_2Eextreal__le,axiom,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__le) ).
fof(conj_thm_2Eextreal_2Emax__le,conjecture,
! [X22] :
( mem(X22,ty_2Eextreal_2Eextreal)
=> ! [X23] :
( mem(X23,ty_2Eextreal_2Eextreal)
=> ! [X24] :
( mem(X24,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,X23),X24)),X22))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X23),X22))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X24),X22)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Emax__le) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(conj_thm_2Eextreal_2Ele__total,axiom,
! [X13] :
( mem(X13,ty_2Eextreal_2Eextreal)
=> ! [X14] :
( mem(X14,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X14))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X14),X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__total) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
fof(ax_thm_2Eextreal_2Eextreal__max__def,axiom,
! [X13] :
( mem(X13,ty_2Eextreal_2Eextreal)
=> ! [X14] :
( mem(X14,ty_2Eextreal_2Eextreal)
=> ap(ap(c_2Eextreal_2Eextreal__max,X13),X14) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X13),X14)),X14),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eextreal_2Eextreal__max__def) ).
fof(conj_thm_2Eextreal_2Ele__trans,axiom,
! [X13] :
( mem(X13,ty_2Eextreal_2Eextreal)
=> ! [X14] :
( mem(X14,ty_2Eextreal_2Eextreal)
=> ! [X18] :
( mem(X18,ty_2Eextreal_2Eextreal)
=> ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X14))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X14),X18)) )
=> p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X18)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__trans) ).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,X9)
=> ! [X11] :
( mem(X11,X9)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2ET),X10),X11) = X10
& ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2EF),X10),X11) = X11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
fof(ne_ty_2Eextreal_2Eextreal,axiom,
ne(ty_2Eextreal_2Eextreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Eextreal_2Eextreal) ).
fof(mem_c_2Eextreal_2Eextreal__max,axiom,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__max) ).
fof(c_0_14,plain,
! [X27,X28,X29,X30] :
( ~ mem(X29,arr(X27,X28))
| ~ mem(X30,X27)
| mem(ap(X29,X30),X28) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
fof(c_0_15,plain,
! [X31,X32] :
( ( ~ p(X31)
| ~ p(X32)
| X31 = X32
| ~ mem(X32,bool)
| ~ mem(X31,bool) )
& ( p(X31)
| p(X32)
| X31 = X32
| ~ mem(X32,bool)
| ~ mem(X31,bool) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])]) ).
fof(c_0_16,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
cnf(c_0_17,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
inference(split_conjunct,[status(thm)],[mem_c_2Eextreal_2Eextreal__le]) ).
fof(c_0_19,negated_conjecture,
~ ! [X22] :
( mem(X22,ty_2Eextreal_2Eextreal)
=> ! [X23] :
( mem(X23,ty_2Eextreal_2Eextreal)
=> ! [X24] :
( mem(X24,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,X23),X24)),X22))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X23),X22))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X24),X22)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eextreal_2Emax__le]) ).
cnf(c_0_20,plain,
( p(X1)
| p(X2)
| X1 = X2
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_22,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,X1),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_24,plain,
! [X76,X77] :
( ~ mem(X76,ty_2Eextreal_2Eextreal)
| ~ mem(X77,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X76),X77))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X77),X76)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__total])])]) ).
fof(c_0_25,negated_conjecture,
( mem(esk3_0,ty_2Eextreal_2Eextreal)
& mem(esk4_0,ty_2Eextreal_2Eextreal)
& mem(esk5_0,ty_2Eextreal_2Eextreal)
& ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) )
& ( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) )
& ( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_26,plain,
( X1 = c_2Ebool_2EF
| p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_27,plain,
( mem(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2),bool)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_28,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X1))
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
mem(esk5_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ p(X1)
| ~ p(X2)
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,plain,
mem(c_2Ebool_2ET,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET]) ).
cnf(c_0_32,plain,
p(c_2Ebool_2ET),
inference(split_conjunct,[status(thm)],[ax_true_p]) ).
cnf(c_0_33,plain,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),X1))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
mem(esk3_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( X1 = c_2Ebool_2ET
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_37,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_38,negated_conjecture,
mem(esk4_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
( X1 = ap(ap(c_2Eextreal_2Eextreal__le,X2),X3)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X3))
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X3,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_40,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_41,plain,
! [X78,X79] :
( ~ mem(X78,ty_2Eextreal_2Eextreal)
| ~ mem(X79,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__max,X78),X79) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X78),X79)),X79),X78) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Eextreal_2Eextreal__max__def])])]) ).
cnf(c_0_42,plain,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_44,plain,
! [X73,X74,X75] :
( ~ mem(X73,ty_2Eextreal_2Eextreal)
| ~ mem(X74,ty_2Eextreal_2Eextreal)
| ~ mem(X75,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X73),X74))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X74),X75))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X73),X75)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__trans])])]) ).
cnf(c_0_45,negated_conjecture,
( X1 = ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0))
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35]),c_0_29])]) ).
fof(c_0_46,plain,
! [X66,X67,X68] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X66),c_2Ebool_2ET),X67),X68) = X67
| ~ mem(X68,X66)
| ~ mem(X67,X66)
| ~ ne(X66) )
& ( ap(ap(ap(c_2Ebool_2ECOND(X66),c_2Ebool_2EF),X67),X68) = X68
| ~ mem(X68,X66)
| ~ mem(X67,X66)
| ~ ne(X66) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2ECOND__CLAUSES])])])]) ).
cnf(c_0_47,plain,
( ap(ap(c_2Eextreal_2Eextreal__max,X1),X2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X1),X2)),X2),X1)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2EF
| ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_29]),c_0_38])]) ).
cnf(c_0_49,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X3))
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X3,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0) = c_2Ebool_2ET
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_31]),c_0_32])]) ).
cnf(c_0_51,plain,
( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2EF),X2),X3) = X3
| ~ mem(X3,X1)
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),esk5_0),esk4_0) = ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)
| ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_29]),c_0_38])]) ).
cnf(c_0_53,plain,
ne(ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[ne_ty_2Eextreal_2Eextreal]) ).
cnf(c_0_54,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0) = c_2Ebool_2ET
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_29]),c_0_35])]) ).
cnf(c_0_55,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_56,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_38]),c_0_29]),c_0_53])]) ).
cnf(c_0_57,negated_conjecture,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_58,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_48]),c_0_38])]),c_0_22]) ).
cnf(c_0_59,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,plain,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(split_conjunct,[status(thm)],[mem_c_2Eextreal_2Eextreal__max]) ).
cnf(c_0_63,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_32])]),c_0_59]) ).
cnf(c_0_64,plain,
( mem(ap(c_2Eextreal_2Eextreal__max,X1),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_17,c_0_62]) ).
cnf(c_0_65,plain,
( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2ET),X2),X3) = X2
| ~ mem(X3,X1)
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_66,negated_conjecture,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),esk5_0),esk4_0) = ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_63]),c_0_29]),c_0_38])]) ).
cnf(c_0_67,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)))
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0),ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_55]),c_0_35])]) ).
cnf(c_0_68,plain,
( mem(ap(ap(c_2Eextreal_2Eextreal__max,X1),X2),ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_17,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_70,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_38]),c_0_29]),c_0_53])]) ).
cnf(c_0_71,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_29]),c_0_38])]) ).
cnf(c_0_72,negated_conjecture,
p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_71]),c_0_38])]) ).
cnf(c_0_74,negated_conjecture,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_70]),c_0_72]),c_0_72])]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_63]),c_0_32])]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP021+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30 % Computer : n008.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sun Aug 27 16:11:17 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.15/0.46 start to proof: theBenchmark
% 5.03/5.22 % Version : CSE_E---1.5
% 5.03/5.22 % Problem : theBenchmark.p
% 5.03/5.22 % Proof found
% 5.03/5.22 % SZS status Theorem for theBenchmark.p
% 5.03/5.22 % SZS output start Proof
% See solution above
% 5.03/5.23 % Total time : 4.708000 s
% 5.03/5.23 % SZS output end Proof
% 5.03/5.23 % Total time : 4.711000 s
%------------------------------------------------------------------------------